Sodium pumps adapt spike bursting to stimulus statistics

Bursting Dynamics Based on the Persistent Na+ and Na+/K+ Pump Currents: A Dynamic Clamp Approach

Life-supporting rhythmic motor functions like heart-beating in invertebrates and breathing in vertebrates require an indefatigable generation of a robust rhythm by specialized oscillatory circuits, central pattern generators (CPGs). These CPGs should be sufficiently flexible to adjust to environmental changes and behavioral goals. Continuous self-sustained operation of bursting neurons requires intracellular Na+ concentration to remain in a functional range and to have checks and balances of the Na+ fluxes met on a cycle-to-cycle basis during bursting. We hypothesize that at a high excitability state, the interaction of the Na+/K+ pump current, Ipump, and persistent Na+ current, INaP, produces a mechanism supporting functional bursting. INaP is a low voltage-activated inward current that initiates and supports the bursting phase. This current does not inactivate and is a significant source of Na+ influx. Ipump is an outward current activated by [Na+]i and is the major source of Na+ efflux. Both currents are active and counteract each other between and during bursts. We apply a combination of electrophysiology, computational modeling, and dynamic clamp to investigate the role of Ipump and INaP in the leech heartbeat CPG interneurons (HN neurons). Applying dynamic clamp to introduce additional Ipump and INaP into the dynamics of living synaptically isolated HN neurons in real time, we show that their joint increase produces transition into a new bursting regime characterized by higher spike frequency and larger amplitude of the membrane potential oscillations. Further increase of Ipump speeds up this rhythm by shortening burst duration (BD) and interburst interval (IBI).

Biophysical models of intrinsic homeostasis: Firing rates and beyond

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.

Comodulation of h- and Na+/K+ Pump Currents Expands the Range of Functional Bursting in a Central Pattern Generator by Navigating between Dysfunctional Regimes

Central pattern generators (CPGs), specialized oscillatory neuronal networks controlling rhythmic motor behaviors such as breathing and locomotion, must adjust their patterns of activity to a variable environment and changing behavioral goals. Neuromodulation adjusts these patterns by orchestrating changes in multiple ionic currents. In the medicinal leech, the endogenous neuromodulator myomodulin speeds up the heartbeat CPG by reducing the electrogenic Na+/K+ pump current and increasing h-current in pairs of mutually inhibitory leech heart interneurons (HNs), which form half-center oscillators (HN HCOs). Here we investigate whether the comodulation of two currents could have advantages over a single current in the control of functional bursting patterns of a CPG. We use a conductance-based biophysical model of an HN HCO to explain the experimental effects of myomodulin. We demonstrate that, in the model, comodulation of the Na+/K+ pump current and h-current expands the range of functional bursting activity by avoiding transitions into nonfunctional regimes, such as asymmetric bursting and plateau-containing seizure-like activity. We validate the model by finding parameters that reproduce temporal bursting characteristics matching experimental recordings from HN HCOs under control, three different myomodulin concentrations, and Cs+ treated conditions. The matching cases are located along the border of an asymmetric regime away from the border with more dangerous seizure-like activity. We found a simple comodulation mechanism with an inverse relation between the pump and h-currents makes a good fit of the matching cases and comprises a general mechanism for the robust and flexible control of oscillatory neuronal networks.SIGNIFICANCE STATEMENT Rhythm-generating neuronal circuits adjust their oscillatory patterns to accommodate a changing environment through neuromodulation. In different species, chemical messengers participating in such processes may target two or more membrane currents. In medicinal leeches, the neuromodulator myomodulin speeds up the heartbeat central pattern generator by reducing Na+/K+ pump current and increasing h-current. In a computational model, we show that this comodulation expands the range of central pattern generator's functional activity by navigating the circuit between dysfunctional regimes resulting in a much wider range of cycle period. This control would not be attainable by modulating only one current, emphasizing the synergy of combined effects. Given the prevalence of h-current and Na+/K+ pump current in neurons, similar comodulation mechanisms may exist across species.

Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type

During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we investigated the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect typically attributed solely to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Thus, individual neurons may respond very differently to the same input stimuli, depending on their recent patterns of activity and/or the current brain-state.

Ionic concentrations in the brain are not constant. We show that during intense neuronal activity, they can change on the order of seconds and even switch neuronal spiking patterns under identical stimulation from a regular firing mode to an intermittently interrupted one. Triggered by an accumulation of extracellular potassium, such a transition is caused by a specific, qualitative change in of the neuronal voltage dynamics—a so-called bifurcation—which affects crucial features of action-potential generation and bears consequences for how information is encoded and how neurons behave together in the network. Also, changes in intracellular sodium can induce measurable effects, like a reduction of spike amplitude that occurs independently of the fast amplitude effects attributed to sodium channel inactivation. Taken together, our results demonstrate that a neuron can respond very differently to the same stimulus, depending on its previous activity or the current brain state. This finding may be particularly relevant when other regulatory mechanisms of ionic homeostasis are challenged, for example, during pathological states of glial impairment or oxygen deprivation. Finally, categorization of cortical neurons as intrinsically bursting or regular spiking may be biased by the ionic concentrations at the time of the observation, highlighting the non-static nature of neuronal dynamics.

Na+-K+-ATPase functions in the developing hippocampus: regional differences in CA1 and CA3 neuronal excitability and role in epileptiform network bursting

The Na⁺-K⁺-ATPase (Na⁺-K⁺ pump) is essential for setting resting membrane potential and restoring transmembrane Na⁺ and K⁺ gradients after neuronal firing, yet its roles in developing neurons are not well understood. This study examined the contribution of the Na⁺-K⁺ pump to resting membrane potential and membrane excitability of developing CA1 and CA3 neurons and its role in maintaining synchronous network bursting. Experiments were conducted in postnatal day (P)9 to P13 rat hippocampal slices using whole cell patch-clamp and extracellular field-potential recordings. Blockade of the Na⁺-K⁺ pump with strophanthidin caused marked depolarization (23.1 mV) in CA3 neurons but only a modest depolarization (3.3 mV) in CA1 neurons. Regarding other membrane properties, strophanthidin differentially altered the voltage-current responses, input resistance, action-potential threshold and amplitude, rheobase, and input-output relationship in CA3 vs. CA1 neurons. At the network level, strophanthidin stopped synchronous epileptiform bursting in CA3 induced by 0 Mg²⁺ and 4-aminopyridine. Furthermore, dual whole cell recordings revealed that strophanthidin disrupted the synchrony of CA3 neuronal firing. Finally, strophanthidin reduced spontaneous excitatory postsynaptic current (sEPSC) bursts (i.e., synchronous transmitter release) and transformed them into individual sEPSC events (i.e., nonsynchronous transmitter release). These data suggest that the Na⁺-K⁺ pump plays a more profound role in membrane excitability in developing CA3 neurons than in CA1 neurons and that the pump is essential for the maintenance of synchronous network bursting in CA3. Compromised Na⁺-K⁺ pump function leads to cessation of ongoing synchronous network activity, by desynchronizing neuronal firing and neurotransmitter release in the CA3 synaptic network. These findings have implications for the regulation of network excitability and seizure generation in the developing brain.NEW & NOTEWORTHY Despite the extensive literature showing the importance of the Na⁺-K⁺ pump in various neuronal functions, its roles in the developing brain are not well understood. This study reveals that the Na⁺-K⁺ pump differentially regulates the excitability of CA3 and CA1 neurons in the developing hippocampus, and the pump activity is crucial for maintaining network activity. Compromised Na⁺-K⁺ pump activity desynchronizes neuronal firing and transmitter release, leading to cessation of ongoing epileptiform network bursting.

Integrative analysis of in vivo recording with single-cell RNA-seq data reveals molecular properties of light-sensitive neurons in mouse V1

Vision formation is classically based on projections from retinal ganglion cells (RGC) to the lateral geniculate nucleus (LGN) and the primary visual cortex (V1). Neurons in the mouse V1 are tuned to light stimuli. Although the cellular information of the retina and the LGN has been widely studied, the transcriptome profiles of single light-stimulated neuron in V1 remain unknown. In our study, in vivo calcium imaging and whole-cell electrophysiological patch-clamp recording were utilized to identify 53 individual cells from layer 2/3 of V1 as light-sensitive (LS) or non-light-sensitive (NS) by single-cell light-evoked calcium evaluation and action potential spiking. The contents of each cell after functional tests were aspirated in vivo through a patch-clamp pipette for mRNA sequencing. Moreover, the three-dimensional (3-D) morphological characterizations of the neurons were reconstructed in a live mouse after the whole-cell recordings. Our sequencing results indicated that V1 neurons with a high expression of genes related to transmission regulation, such as Rtn4r and Rgs7, and genes involved in membrane transport, such as Na⁺/K⁺ ATPase and NMDA-type glutamatergic receptors, preferentially responded to light stimulation. Furthermore, an antagonist that blocks Rtn4r signals could inactivate the neuronal responses to light stimulation in live mice. In conclusion, our findings of the vivo-seq analysis indicate the key role of the strength of synaptic transmission possesses neurons in V1 of light sensory.

Origin of slow spontaneous resting-state neuronal fluctuations in brain networks

Resting- or baseline-state low-frequency (0.01-0.2 Hz) brain activity is observed in fMRI, EEG, and local field potential recordings. These fluctuations were found to be correlated across brain regions and are thought to reflect neuronal activity fluctuations between functionally connected areas of the brain. However, the origin of these infra-slow resting-state fluctuations remains unknown. Here, using a detailed computational model of the brain network, we show that spontaneous infra-slow (<0.05 Hz) activity could originate due to the ion concentration dynamics. The computational model implemented dynamics for intra- and extracellular K⁺ and Na⁺ and intracellular Cl^- ions, Na⁺/K⁺ exchange pump, and KCC2 cotransporter. In the network model simulating resting awake-like brain state, we observed infra-slow fluctuations in the extracellular K⁺ concentration, Na⁺/K⁺ pump activation, firing rate of neurons, and local field potentials. Holding K⁺ concentration constant prevented generation of the infra-slow fluctuations. The amplitude and peak frequency of this activity were modulated by the Na⁺/K⁺ pump, AMPA/GABA synaptic currents, and glial properties. Further, in a large-scale network with long-range connections based on CoCoMac connectivity data, the infra-slow fluctuations became synchronized among remote clusters similar to the resting-state activity observed in vivo. Overall, our study proposes that ion concentration dynamics mediated by neuronal and glial activity may contribute to the generation of very slow spontaneous fluctuations of brain activity that are reported as the resting-state fluctuations in fMRI and EEG recordings.

Sodium pump regulation of locomotor control circuits

Sodium pumps are ubiquitously expressed membrane proteins that extrude three Na⁺ ions in exchange for two K⁺ ions, using ATP as an energy source. Recent studies have illuminated additional, dynamic roles for sodium pumps in regulating the excitability of neuronal networks in an activity-dependent fashion. We review their role in a novel form of short-term memory within rhythmic locomotor networks. The data we review derives mainly from recent studies on Xenopus tadpoles and neonatal mice. The role and underlying mechanisms of pump action broadly match previously published data from an invertebrate, the Drosophila larva. We therefore propose a highly conserved mechanism by which sodium pump activity increases following a bout of locomotion. This results in an ultraslow afterhyperpolarization (usAHP) of the membrane potential that lasts around 1 min, but which only occurs in around half the network neurons. This usAHP in turn alters network excitability so that network output is reduced in a locomotor interval-dependent manner. The pumps therefore confer on spinal locomotor networks a temporary memory trace of recent network performance.

Bursting Neurons in the Hippocampal Formation Encode Features of LFP Rhythms

Burst spike patterns are common in regions of the hippocampal formation such as the subiculum and medial entorhinal cortex (MEC). Neurons in these areas are immersed in extracellular electrical potential fluctuations often recorded as the local field potential (LFP). LFP rhythms within different frequency bands are linked to different behavioral states. For example, delta rhythms are often associated with slow-wave sleep, inactivity and anesthesia; whereas theta rhythms are prominent during awake exploratory behavior and REM sleep. Recent evidence suggests that bursting neurons in the hippocampal formation can encode LFP features. We explored this hypothesis using a two-compartment model of a bursting pyramidal neuron driven by time-varying input signals containing spectral peaks at either delta or theta rhythms. The model predicted a neural code in which bursts represented the instantaneous value, phase, slope and amplitude of the driving signal both in their timing and size (spike number). To verify whether this code is employed in vivo, we examined electrophysiological recordings from the subiculum of anesthetized rats and the MEC of a behaving rat containing prevalent delta or theta rhythms, respectively. In both areas, we found bursting cells that encoded information about the instantaneous voltage, phase, slope and/or amplitude of the dominant LFP rhythm with essentially the same neural code as the simulated neurons. A fraction of the cells encoded part of the information in burst size, in agreement with model predictions. These results provide in-vivo evidence that the output of bursting neurons in the mammalian brain is tuned to features of the LFP.

Mechanisms underlying the activity-dependent regulation of locomotor network performance by the Na+ pump

Activity-dependent modification of neural network output usually results from changes in neurotransmitter release and/or membrane conductance. In Xenopus frog tadpoles, spinal locomotor network output is adapted by an ultraslow afterhyperpolarization (usAHP) mediated by an increase in Na⁺ pump current. Here we systematically explore how the interval between two swimming episodes affects the second episode, which is shorter and slower than the first episode. We find the firing reliability of spinal rhythmic neurons to be lower in the second episode, except for excitatory descending interneurons (dINs). The sodium/proton antiporter, monensin, which potentiates Na⁺ pump function, induced similar effects to short inter-swim intervals. A usAHP induced by supra-threshold pulses reduced neuronal firing reliability during swimming. It also increased the threshold current for spiking and introduced a delay to the first spike in a train, without reducing subsequent firing frequency. This delay was abolished by ouabain or zero K⁺ saline, which eliminate the usAHP. We present evidence for an A-type K⁺ current in spinal CPG neurons which is inactivated by depolarization and de-inactivated by hyperpolarization, and accounts for the prolonged delay. We conclude that the usAHP attenuates neuronal responses to excitatory network inputs by both membrane hyperpolarization and enhanced de-inactivation of an A-current.

Electrogenic properties of the Na⁺/K⁺ ATPase control transitions between normal and pathological brain states

Ionic concentrations fluctuate significantly during epileptic seizures. In this study, using a combination of in vitro electrophysiology, computer modeling, and dynamical systems analysis, we demonstrate that changes in the potassium and sodium intra- and extracellular ion concentrations ([K(+)] and [Na(+)], respectively) during seizure affect the neuron dynamics by modulating the outward Na(+)/K(+) pump current. First, we show that an increase of the outward Na(+)/K(+) pump current mediates termination of seizures when there is a progressive increase in the intracellular [Na(+)]. Second, we show that the Na(+)/K(+) pump current is crucial in maintaining the stability of the physiological network state; a reduction of this current leads to the onset of seizures via a positive-feedback loop. We then present a novel dynamical mechanism for bursting in neurons with a reduced Na(+)/K(+) pump. Overall, our study demonstrates the profound role of the current mediated by Na(+)/K(+) ATPase on the stability of neuronal dynamics that was previously unknown.

Intracellular calcium dynamics permit a Purkinje neuron model to perform toggle and gain computations upon its inputs

Without synaptic input, Purkinje neurons can spontaneously fire in a repeating trimodal pattern that consists of tonic spiking, bursting and quiescence. Climbing fiber input (CF) switches Purkinje neurons out of the trimodal firing pattern and toggles them between a tonic firing and a quiescent state, while setting the gain of their response to Parallel Fiber (PF) input. The basis to this transition is unclear. We investigate it using a biophysical Purkinje cell model under conditions of CF and PF input. The model can replicate these toggle and gain functions, dependent upon a novel account of intracellular calcium dynamics that we hypothesize to be applicable in real Purkinje cells.

Linking dynamical and functional properties of intrinsically bursting neurons

Several studies have shown that bursting neurons can encode information in the number of spikes per burst: As the stimulus varies, so does the length of individual bursts. There presented stimuli, however, vary substantially among different sensory modalities and different neurons.The goal of this paper is to determine which kind of stimulus features can be encoded in burst length, and how those features depend on the mathematical properties of the underlying dynamical system.We show that the initiation and termination of each burst is triggered by specific stimulus features whose temporal characteristsics are determined by the types of bifurcations that initiate and terminate firing in each burst. As only a few bifurcations are possible, only a restricted number of encoded features exists. Here we focus specifically on describing parabolic, square-wave and elliptic bursters. We find that parabolic bursters, whose firing is initiated and terminated by saddle-node bifurcations, behave as prototypical integrators: Firing is triggered by depolarizing stimuli, and lasts for as long as excitation is prolonged. Elliptic bursters, contrastingly, constitute prototypical resonators, since both the initiating and terminating bifurcations possess well-defined oscillation time scales. Firing is therefore triggered by stimulus stretches of matching frequency and terminated by a phase-inversion in the oscillation. The behavior of square-wave bursters is somewhat intermediate, since they are triggered by a fold bifurcation of cycles of well-defined frequency but are terminated by a homoclinic bifurcation lacking an oscillating time scale. These correspondences show that stimulus selectivity is determined by the type of bifurcations. By testing several neuron models, we also demonstrate that additional biological properties that do not modify the bifurcation structure play a minor role in stimulus encoding. Moreover, we show that burst-length variability (and thereby, the capacity to transmit information) depends on a trade-off between the variance of the external signal driving the cell and the strength of the slow internal currents modulating bursts. Thus, our work explicitly links the computational properties of bursting neurons to the mathematical properties of the underlying dynamical systems.

The sodium-potassium pump controls the intrinsic firing of the cerebellar Purkinje neuron

In vitro, cerebellar Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting, and quiescence. The bimodal pattern consists of tonic spiking and quiescence. It is unclear how these firing patterns are generated and what determines which firing pattern is selected. We have constructed a realistic biophysical Purkinje cell model that can replicate these patterns. In this model, Na(+)/K(+) pump activity sets the Purkinje cell's operating mode. From rat cerebellar slices we present Purkinje whole cell recordings in the presence of ouabain, which irreversibly blocks the Na(+)/K(+) pump. The model can replicate these recordings. We propose that Na(+)/K(+) pump activity controls the intrinsic firing mode of cerbellar Purkinje cells.

Dopaminergic modulation of mitral cells and odor responses in the zebrafish olfactory bulb

In the olfactory bulb, the modulatory neurotransmitter dopamine (DA) is coexpressed with GABA by local interneurons, but its role in odor processing remains obscure. We examined functions of DA mediated by D₂-like receptors in the olfactory bulb of adult zebrafish by pharmacology, whole-cell recordings, calcium imaging, and optogenetics. Bath application of DA had no detectable effect on odorant-evoked sensory input. DA directly hyperpolarized mitral cells (MCs) via D₂-like receptors and slightly increased their response gain. Consistent with this effect on input-output functions of MCs, small odorant responses were suppressed, whereas strong responses were enhanced in the presence of DA. These effects increased the root-mean-square contrast of population activity patterns but did not reduce their correlations. Optical stimulation of interneurons expressing channelrhodopsin-2 evoked fast GABAergic inhibitory currents in mitral cells but failed to activate D₂ receptor-mediated currents when stimuli were short. Prolonged stimulus trains, however, activated a slow hyperpolarizing current that was blocked by an antagonist of D₂-like receptors. GABA and DA are therefore both released from interneurons by electrical activity and hyperpolarize MCs, but D₂-dependent dopaminergic effects occur on slower timescales. Additional effects of DA may be mediated by D₁-like receptors. These results indicate that DA acts on D₂-like receptors via asynchronous release and/or volume transmission and implicate DA in the slow adaptation of circuit function. The shift of the membrane potential away from spike threshold could adapt mitral cells to background input without compromising their sensitivity.

Suppression of spikes during posttetanic hyperpolarization in auditory neurons: the role of temperature, I(h) currents, and the Na(+)-K(+)-ATPase pump

In vivo recordings from postsynaptic neurons in the medial nucleus of the trapezoid body (MNTB), an auditory brain stem nucleus, show that acoustic stimulation produces a burst of spikes followed by a period of hyperpolarization and suppressed spiking activity. The underlying mechanism for this hyperpolarization and reduced spiking is unknown. Furthermore, the mechanisms that control excitability and resting membrane potential are not fully determined for these MNTB neurons. In this study we investigated the excitability of principal neurons from the MNTB after high-frequency afferent fiber stimulation, using whole cell recordings from postnatal day 15-17 rat brain stem slices. We found that Na(+)-K(+)-ATPase activity mediates a progressive hyperpolarization during a prolonged tetanic train and a posttetanic hyperpolarization (PTH) at the end of the train, when postsynaptic action potentials failed to fire. Raising the temperature to more physiological levels (from 22 to 35°C) depolarized the resting membrane potential of both presynaptic and postsynaptic cells and decreased the latency of action potential firing during PTH. Higher temperatures also reduced the presynaptic calyx action potential failure rates by 50% during presynaptic PTH, thus increasing the safety-factor for presynaptic spiking. The effect of temperature on hyperpolarization-activated cation current (I(h)) is reflected in the resting potential at both pre- and postsynaptic neurons. We thus propose that temperature-sensitive Na(+)-K(+)-ATPase activity and I(h) contribute to set the resting membrane potential and produce a brief period of suppressed spiking (or action potential failures) after a prolonged high-frequency afferent tetanus.

Natural movies evoke spike trains with low spike time variability in cat primary visual cortex

Neuronal responses in primary visual cortex have been found to be highly variable. This has led to the widespread notion that neuronal responses have to be averaged over large numbers of neurons to obtain suitably invariant responses that can be used to reliably encode or represent external stimuli. However, it is possible that the high variability of neuronal responses may result from the use of simple, artificial stimuli and that the visual cortex may respond differently to dynamic, naturalistic images. To investigate this question, we recorded the responses of primary visual cortical neurons in the anesthetized cat under stimulation with time-varying natural movies. We found that cortical neurons on the whole exhibited a high degree of spike count variability, but a surprisingly low degree of spike time variability. The spike count variability was further reduced when all but the first spike in a burst were removed. We also found that responses exhibiting low spike time variability exhibited low spike count variability, suggesting that rate coding and temporal coding might be more compatible than previously thought. In addition, we found the spike time variability to be significantly lower when stimulated by natural movies as compared with stimulation using drifting gratings. Our results indicate that response variability in primary visual cortex is stimulus dependent and significantly lower than previous measurements have indicated.

In vivo conditions influence the coding of stimulus features by bursts of action potentials

The functional role of burst firing (i.e. the firing of packets of action potentials followed by quiescence) in sensory processing is still under debate. Should bursts be considered as unitary events that signal the presence of a particular feature in the sensory environment or is information about stimulus attributes contained within their temporal structure? We compared the coding of stimulus attributes by bursts in vivo and in vitro of electrosensory pyramidal neurons in weakly electric fish by computing correlations between burst and stimulus attributes. Our results show that, while these correlations were strong in magnitude and significant in vitro, they were actually much weaker in magnitude if at all significant in vivo. We used a mathematical model of pyramidal neuron activity in vivo and showed that such a model could reproduce the correlations seen in vitro, thereby suggesting that differences in burst coding were not due to differences in bursting seen in vivo and in vitro. We next tested whether variability in the baseline (i.e. without stimulation) activity of ELL pyramidal neurons could account for these differences. To do so, we injected noise into our model whose intensity was calibrated to mimic baseline activity variability as quantified by the coefficient of variation. We found that this noise caused significant decreases in the magnitude of correlations between burst and stimulus attributes and could account for differences between in vitro and in vivo conditions. We then tested this prediction experimentally by directly injecting noise in vitro through the recording electrode. Our results show that this caused a lowering in magnitude of the correlations between burst and stimulus attributes in vitro and gave rise to values that were quantitatively similar to those seen under in vivo conditions. While it is expected that noise in the form of baseline activity variability will lower correlations between burst and stimulus attributes, our results show that such variability can account for differences seen in vivo. Thus, the high variability seen under in vivo conditions has profound consequences on the coding of information by bursts in ELL pyramidal neurons. In particular, our results support the viewpoint that bursts serve as a detector of particular stimulus features but do not carry detailed information about such features in their structure.

The structure and size of sensory bursts encode stimulus information but only size affects behavior

Cricket ultrasound avoidance is a classic model system for neuroethology. Avoidance steering is triggered by high-firing-rate bursts of spikes in the auditory command neuron AN2. Although bursting is common among sensory neurons, and although the detailed structure of bursts may encode information about the stimulus, it is as yet unclear whether this information is decoded. We address this question in two ways: from an information coding point of view, by showing the relationship between stimulus and burst structure; and also from a functional point of view by showing the relationship between burst structure and behavior. We conclude that the burst structure carries detailed temporal information about the stimulus but that this has little impact on the behavioral response, which is affected mainly by burst size.

Spike integration and cellular memory in a rhythmic network from Na+/K+ pump current dynamics

The output of a neural circuit results from an interaction between the intrinsic properties of neurons within the circuit and the features of the synaptic connections between them. The plasticity of intrinsic properties has been primarily attributed to modification of ion channel function and/or number. In this study, we demonstrate a mechanism for intrinsic plasticity in rhythmically active Drosophila neurons that is not conductance-based. Larval motor neurons show a long lasting sodium-dependent afterhyperpolarization (AHP) following bursts of action potentials that is mediated by the electrogenic activity of Na⁺/K⁺ ATPase. This AHP persists for multiple seconds following volleys of action potentials and is able to function as a pattern-insensitive integrator of spike number that is independent of external calcium. This current also interacts with endogenous Shal K⁺ conductances to modulate spike timing for multiple seconds following rhythmic activity, providing a cellular memory of network activity on a behaviorally relevant time scale.

The information transmitted by spike patterns in single neurons

Spike patterns have been reported to encode sensory information in several brain areas. Here we assess the role of specific patterns in the neural code, by comparing the amount of information transmitted with different choices of the readout neural alphabet. This allows us to rank several alternative alphabets depending on the amount of information that can be extracted from them. One can thereby identify the specific patterns that constitute the most prominent ingredients of the code. We finally discuss the interplay of categorical and temporal information in the amount of synergy or redundancy in the neural code.

Bursts generate a non-reducible spike-pattern code

At the single-neuron level, precisely timed spikes can either constitute firing-rate codes or spike-pattern codes that utilize the relative timing between consecutive spikes. There has been little experimental support for the hypothesis that such temporal patterns contribute substantially to information transmission. By using grasshopper auditory receptors as a model system, we show that correlations between spikes can be used to represent behaviorally relevant stimuli. The correlations reflect the inner structure of the spike train: a succession of burst-like patterns. We demonstrate that bursts with different spike counts encode different stimulus features, such that about 20% of the transmitted information corresponds to discriminating between different features, and the remaining 80% is used to allocate these features in time. In this spike-pattern code, the what and the when of the stimuli are encoded in the duration of each burst and the time of burst onset, respectively. Given the ubiquity of burst firing, we expect similar findings also for other neural systems.

Timescale-invariant representation of acoustic communication signals by a bursting neuron

Acoustic communication often involves complex sound motifs in which the relative durations of individual elements, but not their absolute durations, convey meaning. Decoding such signals requires an explicit or implicit calculation of the ratios between time intervals. Using grasshopper communication as a model, we demonstrate how this seemingly difficult computation can be solved in real time by a small set of auditory neurons. One of these cells, an ascending interneuron, generates bursts of action potentials in response to the rhythmic syllable-pause structure of grasshopper calls. Our data show that these bursts are preferentially triggered at syllable onset; the number of spikes within the burst is linearly correlated with the duration of the preceding pause. Integrating the number of spikes over a fixed time window therefore leads to a total spike count that reflects the characteristic syllable-to-pause ratio of the species while being invariant to playing back the call faster or slower. Such a timescale-invariant recognition is essential under natural conditions, because grasshoppers do not thermoregulate; the call of a sender sitting in the shade will be slower than that of a grasshopper in the sun. Our results show that timescale-invariant stimulus recognition can be implemented at the single-cell level without directly calculating the ratio between pulse and interpulse durations.

Adaptation in multisensory neurons: impact on cross-modal enhancement

Adaptation is a ubiquitous property of sensory neurons. Multisensory neurons, receiving convergent input from different sensory modalities, also likely exhibit adaptation. The responses of multisensory superior colliculus neurons have been extensively studied, but the impact of adaptation on these responses has not been examined. Multisensory neurons in the superior colliculus exhibit cross-modal enhancement, an often non-linear and non-additive increase in response when a stimulus in one modality is paired with a stimulus in a different modality. We examine the possible impact of adaptation on cross-modal enhancement within the framework of a simple model of adaptation for a neuron employing a saturating, logistic response function. We consider how adaptation to an input's mean and standard deviation affects cross-modal enhancement, and also how the statistical correlations between two different modalities influence cross-modal enhancement. We determine the optimal bimodal stimuli to present a bimodal neuron that evoke the largest changes in cross-modal enhancement under adaptation to input statistics. The model requires separate gains for each modality, unless the statistics specific to each modality have been standardised by prior adaptation in earlier, unisensory neurons. The model also predicts that increasing the correlation coefficient between two modalities reduces a multisensory neuron's overall gain.

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate versus current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.

Many neurons are known to achieve a wide dynamic range by adaptively changing their computational input/output function according to the input statistics. These adaptive changes can be very rapid, and it has been suggested that a component of this adaptation could be purely input-driven: even a fixed neural system can show apparent adaptive behavior since inputs with different statistics interact with the nonlinearity of the system in different ways. In this paper, we show how a single neuron's intrinsic computational function can dictate such input-driven changes in its response to varying input statistics, which begets a relationship between two different characterizations of neural function—in terms of mean firing rate and in terms of generating precise spike timing. We then apply our results to two biophysically defined model neurons, which have significantly different response patterns to inputs with various statistics. Our model of intrinsic adaptation explains their behaviors well. Contrary to the picture that neurons carry out a stereotyped computation on their inputs, our results show that even in the simplest cases they have simple yet effective mechanisms by which they can adapt to their input. Adaptation to stimulus statistics, therefore, is built into the most basic single neuron computations.

Visual coding in locust photoreceptors

Information capture by photoreceptors ultimately limits the quality of visual processing in the brain. Using conventional sharp microelectrodes, we studied how locust photoreceptors encode random (white-noise, WN) and naturalistic (1/f stimuli, NS) light patterns in vivo and how this coding changes with mean illumination and ambient temperature. We also examined the role of their plasma membrane in shaping voltage responses. We found that brightening or warming increase and accelerate voltage responses, but reduce noise, enabling photoreceptors to encode more information. For WN stimuli, this was accompanied by broadening of the linear frequency range. On the contrary, with NS the signaling took place within a constant bandwidth, possibly revealing a ‘preference’ for inputs with 1/f statistics. The faster signaling was caused by acceleration of the elementary phototransduction current - leading to bumps - and their distribution. The membrane linearly translated phototransduction currents into voltage responses without limiting the throughput of these messages. As the bumps reflected fast changes in membrane resistance, the data suggest that their shape is predominantly driven by fast changes in the light-gated conductance. On the other hand, the slower bump latency distribution is likely to represent slower enzymatic intracellular reactions. Furthermore, the Q₁₀s of bump duration and latency distribution depended on light intensity. Altogether, this study suggests that biochemical constraints imposed upon signaling change continuously as locust photoreceptors adapt to environmental light and temperature conditions.

An invariance principle for maintaining the operating point of a neuron

Sensory neurons adapt to changes in the natural statistics of their environments through processes such as gain control and firing threshold adjustment. It has been argued that neurons early in sensory pathways adapt according to information-theoretic criteria, perhaps maximising their coding efficiency or information rate. Here, we draw a distinction between how a neuron's preferred operating point is determined and how its preferred operating point is maintained through adaptation. We propose that a neuron's preferred operating point can be characterised by the probability density function (PDF) of its output spike rate, and that adaptation maintains an invariant output PDF, regardless of how this output PDF is initially set. Considering a sigmoidal transfer function for simplicity, we derive simple adaptation rules for a neuron with one sensory input that permit adaptation to the lower-order statistics of the input, independent of how the preferred operating point of the neuron is set. Thus, if the preferred operating point is, in fact, set according to information-theoretic criteria, then these rules nonetheless maintain a neuron at that point. Our approach generalises from the unimodal case to the multimodal case, for a neuron with inputs from distinct sensory channels, and we briefly consider this case too.